CN109145364A - Sensitivity Analysis Method based on Geordie inequality - Google Patents
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Abstract
The disclosure is directed to a kind of Sensitivity Analysis Methods based on Geordie inequality, comprising: according at least one input variable and receptance function, calculate output result；According to output as a result, calculated result Geordie inequality；First input variable is divided into multiple continuous disjoint subintervals, calculates the corresponding first sub- output variable in each subinterval, first input variable is any one input variable at least one input variable；According to each first sub- output variable, corresponding first subbase Buddhist nun's inequality is calculated；According to the result Geordie inequality and the first subbase Buddhist nun's inequality, the corresponding sensitivity of the first input variable is calculated.
Description
Technical field
This disclosure relates to reliability analysis technology field, in particular to a kind of sensitivity based on Geordie inequality point
Analysis method.
Background technique
In the engineering fields such as industrial production and manufacturing and aerospace, product can encounter during design, manufacture, military service
Diversified uncertainty.The output response that these uncertainties being widely present will lead to structure also accordingly exists uncertain
Property, and then the influence that the safety of structure can be generated.Failure probability is probabilistic one of description scheme output response
Characteristic quantity, reliability sensitivity analysis focus on to pay close attention to the uncertain influence to structural realism of input variable.
Currently, Global sensitivity analysis mainly by single output variable model analysis, for multi output variable, by
Often there is stronger correlation in a output variable.Carrying out individual sensitivity analysis for each output variable can ignore not
With the correlation between output variable, so that redundancy occurs in the result of analysis, or even ignore certain important features of output variable
Amount.
It should be noted that information is only used for reinforcing the reason to the background of the disclosure disclosed in above-mentioned background technology part
Solution, therefore may include the information not constituted to the prior art known to persons of ordinary skill in the art.
Summary of the invention
The disclosure is designed to provide a kind of Sensitivity Analysis Method for being based on Geordie (Gini) inequality, and then overcomes needle
The problems of individual sensitivity analysis is carried out to each output variable.
According to one aspect of the disclosure, a kind of Sensitivity Analysis Method is provided, comprising:
According at least an input variable and receptance function, output result is calculated；
According to output as a result, calculated result Geordie inequality；
First input variable is divided into multiple continuous disjoint subintervals, calculates corresponding first son in each subinterval
Output variable, first input variable are any one input variable at least one input variable；
According to each first sub- output variable, corresponding first subbase Buddhist nun's inequality is calculated；
According to the result Geordie inequality and the first subbase Buddhist nun's inequality, it is corresponding sensitive to calculate the first input variable
Degree.
It is counted in the Geordie inequality for calculating output result by formula (1) according to an embodiment of the disclosure
It calculates:
Wherein,For export result Geordie inequality, Y be output as a result, | | | | indicate European norm, y1,
y2,...,yNFor the sample set of Y.
According to an embodiment of the disclosure, the output result includes each input variable at least one input variable
Corresponding output variable.
It is described that first input variable is divided into multiple continuous disjoint subintervals according to an embodiment of the disclosure
Include:
By input variable XiDistributed area be divided into that L is continuous but disjoint subinterval Al=[al-1,al], wherein l
=1,2 ..., L.
It is described in subinterval A according to an embodiment of the disclosurel=[al-1,al] in, Δ a=al-al-1→0。
It is described that corresponding first son in each subinterval is calculated by receptance function respectively according to an embodiment of the disclosure
Output variable includes:
According to input variable XiInterval division, the sample set of output variable is divided into L subset, i.e.,
According to an embodiment of the disclosure, in the first subbase Buddhist nun's inequality for calculating the first sub- output variable
In, it is calculated by formula (2):
Wherein,For first subbase Buddhist nun's inequality, b1...bMFor the corresponding output variable in first of subinterval
Sample set.
It is described according to the Geordie inequality and the first subbase Buddhist nun's inequality according to an embodiment of the disclosure, it calculates
In the corresponding sensitivity of first input variable, calculated by formula (3):
Wherein,For the corresponding sensitivity of the first input variable, PlFirst of subinterval is fallen in for the first input variable
Probability, L are the quantity that the first input variable is divided into continuous disjoint subinterval.
According to an embodiment of the disclosure, PlIt is calculated by formula (4):
For the probability density function of the first input variable,For the cumulative distribution letter of the first input variable
Number.
According to an embodiment of the disclosure, at least one described input variable is close according to the joint probability of input variable
Spend function fX(x) one group of sample { x is generated1,...,xN, wherein N >=1.,
The disclosure provides a kind of Sensitivity Analysis Method based on Geordie inequality, corresponding by least one input variable
How defeated the Geordie inequality calculating for exporting the corresponding first sub- output variable of Geordie inequality and the first input variable subinterval of result is
The global sensitivity of variable out.Avoiding can ignore for the individual sensitivity analysis of each output variable progress in the prior art
Correlation between different output variables so that redundancy occurs in the result of analysis, or even can ignore the certain important of output variable
The problem of characteristic quantity.And it calculates be simple and efficient in the analysis process, sensitivity analysis result is accurate.
It should be understood that above general description and following detailed description be only it is exemplary and explanatory, not
The disclosure can be limited.
Detailed description of the invention
The drawings herein are incorporated into the specification and forms part of this specification, and shows the implementation for meeting the disclosure
Example, and together with specification for explaining the principles of this disclosure.It should be evident that the accompanying drawings in the following description is only the disclosure
Some embodiments for those of ordinary skill in the art without creative efforts, can also basis
These attached drawings obtain other attached drawings.
Fig. 1 is a kind of flow chart for Sensitivity Analysis Method based on Geordie inequality that the embodiment of the present disclosure provides.
Fig. 2 is a kind of sensitivity index for input variable that the embodiment of the present disclosure providesEstimated value with sample number increasing
The variation diagram added.
Specific embodiment
Example embodiment is described more fully with reference to the drawings.However, example embodiment can be with a variety of shapes
Formula is implemented, and is not understood as limited to embodiment set forth herein；On the contrary, thesing embodiments are provided so that the present invention will
Fully and completely, and by the design of example embodiment comprehensively it is communicated to those skilled in the art.Identical attached drawing in figure
Label indicates same or similar structure, thus the detailed description that will omit them.
The result of sensitivity analysis can help researcher to obtain each input variable not know model output variable
Property relative contribution size, obtain the importance ranking of input variable, by distribute more resources to important input variable with
Reduce uncertainty, so as to efficiently reduce the uncertainty of model output variable, to improve the robustness of model
Or the reliability of structure.For unessential input variable, it can be considered as constant processing, thus the simplification of implementation model,
The dimension for reducing input variable facilitates the calculating cost for reducing reliability Optimum Design.As can be seen that sensitivity analysis and can
It is complementary for analyzing by property, and in actual engineering structure, sensitivity analysis receives more and more pay attention to and application.
Sensitivity analysis can be divided into Local sensitivity analysis (Local sensitivity analysis) and overall situation spirit
Basis of sensitivity analysis (Global sensitivity analysis).What local sensitivity usually characterized is when an input variable becomes
Change and other input variables it is fixed when, the situation of change of output variable, mathematically it can be expressed as model output variable pair
Partial derivative of the input variable in set point.There is following defects for local sensitivity: for nonlinear model, can only express mould
Sensitivity information of the type output variable at input variable given value；The variation of single input variable can only once be expressed to model
The influence of output variable, influence of the reciprocation to model output variable between the input variable that is beyond expression.
Relative to local sensitivity, global sensitivity is measured defeated to model when input variable changes in its entire range of distribution
Probabilistic influence of variable out, while the reciprocation between different input variables can also be measured to model output variable
Probabilistic influence.Thus for complicated nonlinear model, input variable is usually measured using Global sensitivity analysis
Relative importance.
In the past few decades, researcher proposes many different Global sensitivity analysis methods, wherein most
Method is suitable for the model with single output variable, and the theoretical system of the Global sensitivity analysis of single output variable has been sent out
Open up fairly perfect.However in actual engineering structure, many models all include multiple people output variable of concern,
Or people's output variable of concern is at any time or space is changed.For at any time or space is changed defeated
Variable out, usually can be by its discrete multiple variable at different moments or different spatial, thus is referred to as below
For multi output variable.
It is for each defeated to its direct method for carrying out Global sensitivity analysis for the model with multi output variable
Variable carries out individual sensitivity analysis out, i.e., repeatedly using existing single output Global sensitivity analysis method.This point
Analysis method can obtain sensitivity of the input variable to different output variables, i.e., input variable to the sensitivity of output variable at any time
Between or space changing rule, so as to obtain influence journey of the input variable to output variable in different time sections or space
Degree.But stronger correlation is usually present between multi output variable, individual sensitivity point is carried out for each output variable
Analysis can ignore the correlation between different output variables, may be such that redundancy occurs in the result of analysis, or even can ignore output
Certain important features of variable.
In the related technology, traditional variance analysis, variation decomposition formula can be regarded as the breakdown for sample statistic,
And full formula of variance can be regarded as the breakdown for variable totality.Similar to variance, Geordie inequality is another common
Estimating for the variability of stochastic variable is measured, compared with variance, the robustness of Geordie inequality is higher, to the susceptibility of exceptional value
It is low, and variable obvious for tail distribution aspect ratio is more effective.
A kind of Sensitivity Analysis Method based on Geordie inequality is provided firstly in this example embodiment, as shown in Figure 1,
Include the following steps:
Step S1 calculates output result according at least an input variable and receptance function；
Step S2, according to output as a result, calculated result Geordie inequality；
First input variable is divided into multiple continuous disjoint subintervals, it is corresponding to calculate each subinterval by step S3
The first sub- output variable, first input variable be at least one input variable in any one input variable；
Step S4 calculates corresponding first subbase Buddhist nun's inequality according to each first sub- output variable；
It is corresponding to calculate the first input variable according to the result Geordie inequality and the first subbase Buddhist nun's inequality by step S5
Sensitivity.
It should be noted that in practical applications, input variable is usually one group of n-dimensional vector, wherein every in n-dimensional vector
One-component is an input variable.
The embodiment of the present disclosure provides a kind of Sensitivity Analysis Method based on Geordie inequality, passes through at least one input variable
The Geordie inequality meter of the corresponding first sub- output variable of Geordie inequality and the first input variable subinterval of corresponding output result
Calculate the global sensitivity of multi output variable.It avoids and carries out individual sensitivity analysis for each output variable in the prior art
The correlation between different output variables can be ignored, so that redundancy occurs in the result of analysis, or even certain of output variable can be ignored
The problem of a little important feature amounts.And it calculates be simple and efficient in the analysis process, sensitivity analysis result is accurate.
The Sensitivity Analysis Method based on Geordie inequality provided below the embodiment of the present disclosure is described in detail:
In step sl, at least one input variable is the joint probability density function f according to input variableX(x) it generates
One group of sample { x1,...,xN, wherein N >=1.Receptance function is the intrinsic input variable and output variable function relationship of system.It can
To be denoted as receptance function Y=g (X), exported by receptance function as a result, exporting includes one group and input sample pair in result
Output sample { the y answered1,...,yN}。
In step s 2, for stochastic variable X, Geordie inequality (Gini ' s Mean Difference) is defined as
G (X)=E | X-X'| (1)
Wherein, X ' is to indicate expectation computing with the independent identically distributed variable of X, E, | | indicate signed magnitude arithmetic(al).With variance
Similar, Geordie inequality (GMD) is estimating for another common variability for measuring stochastic variable.Compared with variance, Geordie is equal
The robustness of difference is higher (low to the susceptibility of exceptional value, and variable obvious for tail distribution aspect ratio is more effective).
For random vector X, the Geordie inequality of broad sense can be similarly defined, i.e.,
G (X)=E | | X-X'| | (2)
Wherein, X' be with the independent identically distributed random vector of X, | | | | indicate European norm.For the sample of random vector X
This collection x1,x2,...,xN, corresponding CMD estimator can be obtained by formula (2) are as follows:
For the output sample { y in step S11,...,yN, it substitutes into formula (3), obtains the Geordie inequality of output result such as
Shown in formula 4:
Wherein,For export result Geordie inequality, Y be output as a result, | | | | indicate European norm, y1,
y2,...,yNFor the sample set of Y.
In step s3, by input variable XiDistributed area be divided into that L is continuous but disjoint subinterval Al=
[al-1,al], wherein l=1,2 ..., L.Wherein, in subinterval Al=[al-1,al] in, Δ a=al-al-1→0。
The corresponding first sub- output variable in each subinterval is calculated, can be and directly calculate each sub-district by receptance function
Between corresponding first sub- output variable；It is also possible to the division rule by input variable, becomes being exported obtained in step S1
Amount is divided, and corresponding first sub- output variable is obtained.
Step S4, by step S3 to each sub- output variable bring into formula (3), obtain formula (5):
Wherein,For first subbase Buddhist nun's inequality, b1...bMFor the corresponding output variable in first of subinterval
Sample set.
In step S5, for polynary receptance function Y=g (X), X=(X1,X2,...,Xd) indicate that d ties up stochastic inputs vector,
Y=(Y1,Y2,...,Ym) indicate that m ties up random output vector.Stochastic inputs variable X1,X2,...,XdIndependently of each other, by its probability
Density function (Probability Density Function)It determines.
As input variable XiIt is confirmed as a certain fixed value xiWhen, the condition Geordie inequality of multivariate model output is expressed as G (Y
|Xi=xi).Input variable XiFixed value xiTo the influential effect of multivariable output can by G (Y) and G (Y | Xi=xi)
Difference is measured, as shown in following formula (10):
d(xi)=G (Y)-G (Y | Xi=xi) (6)
Wherein, d (xi) it is about xiFunction.Due to xiIt is probability density functionThe input variable X of decisioniOne
A fixed value, XiD (x can be passed through for the average influence effect of multivariable outputi) desired value indicate are as follows:
Formula (11), which also illustrates that, works as XiWhen fixed, the average reduction of the Geordie inequality of Y.
For XiMultivariable sensitivity index can by normalized by definition be formula (8):
It indicates to work as input variable XiWhen fixed, the standardization of the variability of model output Y it is expected to reduce.'s
It is worth bigger, expression input variable XiIt is bigger to the influence degree of overall output amount Y.
Conclusion is analyzed according to relevant Distance Components, proposes the decomposition for being similar to the GMD of full formula of variance
Expression formula, as shown in formula (13):
Wherein, ε () indicates energy distance.
It is proved as follows about being discussed in detail for energy distance with the derivation of formula (9):
(1) according to the definition of energy distance, formula (9) is proved:
Due to E | | Y | Xi-Y′|Xi| | only rely upon Xi, E | | Y | X 'i-Y′|X′i| | only rely upon X 'i, therefore formula (11) at
It is vertical, as follows:
Consider X 'iIt is XiAn independent same distribution sample, there is formula (12) to exist:
Therefore formula (11) may be expressed as:
Formula (9) right side of the equal sign second part may be expressed as:
It is therefore writeable on the right side of formula (9) equal sign are as follows:
Due to E | | Y | X-Y ' | X ' | | it may be expressed as:
It is then writeable on the right side of formula (9) equal sign are as follows:
It may also indicate that on the left of formula (9) equal sign are as follows:
Thus it is correct that card formula (9) are obtained.
Formula (7) can be rewritten as following expression according to formula (9):
Therefore, proposed for XiMultivariable global sensitivity index may be expressed as:
Since energy distance can measure the difference of two random vector probability distribution, and ε (Y | Xi,Y′|X′i) can be with
Indicate Y | XiProbability distribution and Y ' | X 'iProbability distribution between difference.It can be seen that according to the definition of Geordie inequalityIt can indicate to work as XiThe variability of the condition distribution of Y when fixed, the difference is that by original
Euclidean distance replaces with energy distance.ThereforeInput variable X can be measurediFor multi output variable
The influence of the overall distribution of Y, this is also indicated that
In the related technology, the main effect sensitivity index based on variance be V [E (and Y | Xi)], indicate output variable Y about Xi
Conditional mean variability (pass through variance measure variability).Thus according to full formula of variance V [E (and Y | Xi)]=V (Y)-E [V
(Y|Xi)] it is found that V [E (Y | Xi)] X is also worked as with measurementiThe average reduction of the variance of Y when fixed.For polynary output variable base
It can be denoted as in the main effect sensitivity index of varianceIt indicates to work as XiThe condition of output variable Y is equal when fixed
The variability of value, variability are measured by variance, which, which also illustrates that, works as XiThe average reduction of the variance of Y when fixed.
The standardized variation decomposition main effect index based on sensitivity analysis are as follows:
WithContrastingly,X is measurediGu the standardized Geordie inequality of timing model output variable Y is averagely reduced
Amount.According to formula (20) it is found thatThe overall distribution situation of multi output result is had also contemplated simultaneously, therefore gets more multi-model
Export probabilistic information.Compared to variance cannot comprehensively presentation model output result variability for,It can be with
Provide a more reasonable, more accurate sensitivity analysis result.
It is the model of scalar for output quantity, formula (9) is still set up.The energy distance of output scalar is represented by random defeated
Enter a kind of Weighted distance between the cumulative distribution function that variable is scalar.Therefore, the sensitivity index proposedIt is applicable in.
According to above content, the estimation method of sensitivity index is proposed.According to the sensitivity definition of formula (8), direct estimationNeed nested sampling.However, the calculating cost of nested sampling is often relatively high.Related researcher proposes one kind
Square independence sensitivity index of the Given-data method for efficiently estimation single input output sample set.Later this method also by
Development is a kind of general sensitivity index estimation method.It will be estimated using Given-data method in the present invention
Assuming that input variable XiCorresponding sample space is [b1,b2], by [b1,b2] to be divided into L continuous but disjoint
Subinterval Al=[al-1,al] (l=1,2 ..., L), wherein b1=a0< a1< ... < al< ... < aL=b2, so as to
To following theorem.
Theorem 1: assuming that receptance function Y=g (X) is the continuous function about X, then whenTend to
When zero, following formula (26) is set up
Wherein, Indicate input variable XiIterated integral
Cloth function.
The proof of theorem 1 is as follows:
First willIt rewrites are as follows:
According to mean value theorem it is found that there are a λl∈[al-1,al] meet
It can thus be appreciated that:
As Δ a → 0, section [al-1,al]→λl.Definition thus according to Riemann integral can obtain following formula establishment:
It brings formula (26) into formula (8), obtains:
Wherein,For the corresponding sensitivity of the first input variable, PlFirst of subinterval is fallen in for the first input variable
Probability, L are the quantity that the first input variable is divided into continuous disjoint subinterval.
PlIt is calculated by formula (4):
For the probability density function of the first input variable,For the cumulative distribution letter of the first input variable
Number.
The corresponding sensitivity of the first input variable is acquired by formula (4), (5), (27) and (28), by selecting different the
One input variable can calculate the corresponding sensitivity of the first input variable of difference.
The same output sample set { y1,...,yNCan be divided into not according to the interval division situation of different input variables
Same subset, thus whole process only needs one group of input-output sample for estimating the corresponding sensitivity of all input variables
Value.Correlative study shows to need the subinterval number to the input variable divided for one group of given input-output sample
Weighed, needs to guarantee that the sample number in subinterval number and each subinterval is enough.Recommend to use Li and Mahadevan
The method of proposition determines subinterval number, i.e.,(expression takesInteger part, N is total number of samples), to reach
The balance of sample number in the subinterval Shuo Hege of subinterval also takes this method in the embodiment of the present disclosure.
The Sensitivity Analysis Method proposed in the embodiment of the present disclosure based on Geordie inequality is carried out below by example
Operation and explanation.
Consider Campbell function as follows:
Wherein, parameter θ value range is -90 ° to 90 °, the corresponding output variable of each value of θ, here, θ's
Value is -90 °, -89 ° ..., 90 °, to have 181 output variables.Input variable a, b, c, d are mutually indepedent and obey area
Between being uniformly distributed in [- 1,5].The value of constant is K1=0.1, K2=0.1.In order to preferably compare and analyze, count first
Each variable let it pass based on sensitivity index proposed in the present inventionEstimated value, while calculating each variable based on variance
Sensitivity indexAs a result as shown in figure 1 and table 1:
Fig. 1 shows the sensitivity index of each variableEstimated value with sample number increased variation diagram.By each in Fig. 1
The corresponding sensitivity lines variation tendency of a variable it is found that the sensitivity index and method for solving proposed with sample number increasing
Add available stable result.
Sensitivity index of each variable of table 1 based on variance and Geordie inequalityEstimated value
Table 1 is directed to each variable, gives the sensitivity index decomposed based on covarianceDetermine with based on Geordie inequality
The sensitivity index of justiceRespective estimated value.The importance of digital representation input variable a, b, c, d in 1 bracket of table are arranged
Sequence.Sensitivity for two kinds of variance measures, the sensitivity of variable d are maximum, this shows variable d to model output result
The overall distribution of variance and model output result has maximum influence.Sensitivity index is decomposed for covarianceB is
Two important variables, followed by a.For the sensitivity index proposedA is the second important variable, followed by b.It is defeated
Two kinds of sensitivity index estimated values for entering variable c are minimum.Based on result above, variable d should more be paid close attention to
To obtain a better model output estimation value.The variable c of influence in view of to(for) model output result is small, can be by c
The uncertainty of multi output variable is not made a significant impact as constant.
Those skilled in the art after considering the specification and implementing the invention disclosed here, will readily occur to its of the disclosure
Its embodiment.This application is intended to cover any variations, uses, or adaptations of the disclosure, these modifications, purposes or
Person's adaptive change follows the general principles of this disclosure and including the undocumented common knowledge in the art of the disclosure
Or conventional techniques.The description and examples are only to be considered as illustrative, and the true scope and spirit of the disclosure are by appended
Claim is pointed out.
Claims (10)
1. a kind of Sensitivity Analysis Method based on Geordie inequality characterized by comprising
According at least one input variable and receptance function, output result is calculated；
According to output as a result, calculated result Geordie inequality；
First input variable is divided into multiple continuous disjoint subintervals, calculates the corresponding first son output in each subinterval
Variable, first input variable are any one input variable at least one input variable；
According to each first sub- output variable, corresponding first subbase Buddhist nun's inequality is calculated；
According to the result Geordie inequality and the first subbase Buddhist nun's inequality, the corresponding sensitivity of the first input variable is calculated.
2. the method as described in claim 1, which is characterized in that in the Geordie inequality for calculating output result, pass through public affairs
Formula (1) calculates:
Wherein,For export result Geordie inequality, Y be output as a result, | | | | indicate European norm, y1,y2,…,yNFor
The sample set of Y.
3. method according to claim 2, which is characterized in that the output result includes each at least one input variable
The corresponding output variable of input variable.
4. method according to claim 2, which is characterized in that it is described first input variable is divided into it is multiple continuous non-intersecting
Subinterval include:
By input variable XiDistributed area be divided into that L is continuous but disjoint subinterval Al=[al-1,al], wherein l=1,
2,...,L。
5. method as claimed in claim 4, which is characterized in that described in subinterval Al=[al-1,al] in, Δ a=al-al-1
→0。
6. method as claimed in claim 4, which is characterized in that described to calculate each subinterval correspondence by receptance function respectively
The first sub- output variable include:
According to input variable XiInterval division, the sample set of output variable is divided into L subset, i.e.,
7. method as claimed in claim 6, which is characterized in that in first subbase for calculating the first sub- output variable
In Buddhist nun's inequality, calculated by formula (2):
Wherein,For first subbase Buddhist nun's inequality, b1...bMFor the sample of the corresponding output variable in first of subinterval
Collection.
8. the method for claim 7, which is characterized in that described equal according to the Geordie inequality and the first subbase Buddhist nun
Difference is calculated in the corresponding sensitivity of the first input variable, is calculated by formula (3):
Wherein,For the corresponding sensitivity of the first input variable, PlThe general of first of subinterval is fallen in for the first input variable
Rate, L are the quantity that the first input variable is divided into continuous disjoint subinterval.
9. method according to claim 8, which is characterized in that PlIt is calculated by formula (4):
For the probability density function of the first input variable,For the cumulative distribution function of the first input variable.
10. the method as described in claim 1, which is characterized in that at least one described input variable is according to input variable
Joint probability density function fX(x) one group of sample { x is generated1,...,xN, wherein N >=1.
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| CN115238528A (en) * | 2022-09-23 | 2022-10-25 | 北京科技大学 | Aircraft structure dynamics parameter sensitivity analysis method based on interval similarity |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004252972A (en) * | 2003-01-31 | 2004-09-09 | Sharp Corp | Device, method, and program for determining input attribute condition, data analyzer, data analysis method, and data analyis program |
| US20070076210A1 (en) * | 2004-08-23 | 2007-04-05 | Palo Alto Research Center Incorporated | Position-based response to light |
| CN105389629A (en) * | 2015-11-10 | 2016-03-09 | 国网四川省电力公司经济技术研究院 | Power grid planning method by combining power grid structural vulnerability |
| CN107516170A (en) * | 2017-08-30 | 2017-12-26 | 东北大学 | A kind of difference self-healing control method based on probability of equipment failure and power networks risk |
| CN107563067A (en) * | 2017-09-06 | 2018-01-09 | 电子科技大学 | Analysis of structural reliability method based on Adaptive proxy model |
| CN107633117A (en) * | 2017-08-25 | 2018-01-26 | 西北工业大学 | Global sensitivity analysis method based on Gaussian process model |
| CN108052767A (en) * | 2017-12-28 | 2018-05-18 | 西北工业大学 | Motion Global sensitivity analysis method |
-
2018
- 2018-07-04 CN CN201810725111.7A patent/CN109145364A/en active Pending
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004252972A (en) * | 2003-01-31 | 2004-09-09 | Sharp Corp | Device, method, and program for determining input attribute condition, data analyzer, data analysis method, and data analyis program |
| US20070076210A1 (en) * | 2004-08-23 | 2007-04-05 | Palo Alto Research Center Incorporated | Position-based response to light |
| CN105389629A (en) * | 2015-11-10 | 2016-03-09 | 国网四川省电力公司经济技术研究院 | Power grid planning method by combining power grid structural vulnerability |
| CN107633117A (en) * | 2017-08-25 | 2018-01-26 | 西北工业大学 | Global sensitivity analysis method based on Gaussian process model |
| CN107516170A (en) * | 2017-08-30 | 2017-12-26 | 东北大学 | A kind of difference self-healing control method based on probability of equipment failure and power networks risk |
| CN107563067A (en) * | 2017-09-06 | 2018-01-09 | 电子科技大学 | Analysis of structural reliability method based on Adaptive proxy model |
| CN108052767A (en) * | 2017-12-28 | 2018-05-18 | 西北工业大学 | Motion Global sensitivity analysis method |
Non-Patent Citations (2)
| Title |
|---|
| SINAN XIAO .ETAL: "Global sensitivity analysis based on Gini’s mean difference", 《STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION》 * |
| 黄莺: "公共建筑火灾风险评估及安全管理方法研究", 《中国博士学位论文全文数据库 (工程科技Ⅱ辑)》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115238528A (en) * | 2022-09-23 | 2022-10-25 | 北京科技大学 | Aircraft structure dynamics parameter sensitivity analysis method based on interval similarity |
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